In the proof of Theorem 10.19, it felt as if not every subset was represented in the function f. Consider for instance {42}. I do not see how the f(x) ever would result {42}. I'm not sure what I am missing. I was also a little confused in the proof for the Schröder-Bernstein Theorem. I must not be keeping my notation straight.
I find it interesting that the cardinality of the real numbers is numerically equivalent to the cardinality of the power set of the natural numbers. I thought that Corollary 10.20 was a nice thought too.
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